Atkin-Lehner |
2+ 3+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312b |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
156672 |
Modular degree for the optimal curve |
Δ |
-934111346688 = -1 · 221 · 36 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 -6 13+ 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3713,99969] |
[a1,a2,a3,a4,a6] |
Generators |
[35:108:1] |
Generators of the group modulo torsion |
j |
-21601086625/3563352 |
j-invariant |
L |
5.150691996947 |
L(r)(E,1)/r! |
Ω |
0.85095128090952 |
Real period |
R |
1.5132158809343 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000054852 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cu1 3666n1 |
Quadratic twists by: -4 8 |